1. Field of the Invention
This invention generally relates to a method and apparatus for sizing and classifying ions suspended in gas based on their ion mobility.
2. Description of the Related Art
The separation and/or sizing of ions according to their different mobilities is widely used for a variety of applications. There term “ion” is used here to include not only molecular ions but also charged particles. Devices that separate ions by their ion mobilities (Z) will be referred to here as “Mobility Analyzers” (MA), even though their use may be more general. Separation of ions in time (SIT) can be achieved in pulsed systems by use of just electric fields. This is the most commonly used technique for ion separation in a gas. Separation in space (SIS) is typically achieved by combining electric and fluid flow fields. SIS mobility analyzers have the advantage of being able to yield monomobile ion fractions which are steady rather than pulsed, and are, therefore, best suited for further use downstream in other instruments. SIS mobility analyzers have been most successful in aerosol separation in the ranges between 10 and a few hundred nm, but is now suitable also to cover the 1-10 nm range at resolutions as high as those typical of the best SIT instruments for ion analysis.
This invention describes some novel designs for SIS type mobility analyzers. Common to all SIS instruments, a small flow of ions is introduced through a narrow slit or small orifice (the “Inlet”) into a much larger laminar flow of sheath gas within a region where the ions move under the simultaneous action of the sheath gas velocity field (U(x)) and the electric field (E(x)), where x is the vector determining position. The sheath gas flow should be substantially ion free. The flow and electric fields are arranged so as to separate the ions by their mobilities (Z). The ion mobility is related to the diffusivity (D)) of the ion by equation 1:Zi=DNe/(kT)  Equation 1.where e is the elementary charge, N is the total number of charges on the ion, K is the Boltzman constant and T is the absolute temperature.
The region in which the separation occurs is referred to as the “Analyzing Region.” The path followed by the ions in this analyzing region is a direct function of the ion's mobility. The term “trajectory” is used here to mean the average path followed by ions with the same Z. Individual Z-ions may deviate from this average path due to diffusion or space charge effects, but the average of all the paths followed by the Z-ions would be the trajectory of the k-ions. The trajectories of very low mobility ions tend to follow the sheath gas flow field (“flow field”) while the trajectories of very high mobility ions tend to follow the electric field. The trajectories of moderate mobility ions are in between these two extremes. After separation, a small fraction of the separated ions pass into an “Outlet.” This outlet may be either a second slit or orifice through which the ions are extracted or a well defined region in which the ion charge is collected. While small flow of gas usually accompanies the ions as they are injected into and/or extracted from the analyzing region, ions may be introduced into or extracted by purely electric means, without a net flow of gas, as for example in the inlets of Strydom R., Leuschner A. H., Stoker P. H. (A Mobility Spectrometer for Measurement of Initial Properties of Po-218, Journal of Aerosol Science, 21 (7): 859-873 1990). Whether an ion is physically extracted from the outlet or extracted bt electrical means, the ion is said to be collected at the outlet. MA devices are usually of one of two types: differential or cumulative. Differential mobility analyzers (DMA) are designed so that ions of different mobilities strike the boundary of the analyzing region at points which are dependent on the ion mobility. An outlet is positioned so that ions within a narrow range of the desired mobility are collected. Cumulative mobility analyzers (CMA) are designed so all or a relatively wide range of ion mobilities above or below a certain critical value reach the outlet.
One goal of MA devices is to spatially separate ions of similar mobilities by the greatest possible distance. The ions move along their trajectories in the analyzing region with a certain velocity. The velocity of an ion is a function of the local values of U(x) and E(x). FIG. 1 is a schematic drawing of a common prior art MA. This MA consists of only two parallel conducting plates: a top plate (110) and a bottom plate (120). These plates will be referred to as elements. The prior art device, therefore, has only two elements: the top element (110) and the bottom element (120). The term “element” can be used interchangeably with the term “electrode.”
A voltage difference (Vc) is placed on the top plate with respect to the bottom plate so that the E(x) field is perpendicular to the plates and acts to push the ions from the top plate to the bottom plate. Sheath gas (150) passes from right to left between the plates so the U(x) field acts to push the ions parallel to the plates from right to left. Hence in this prior art MA, E(x) and U(x) are perpendicular at all points.
In order to analyze the performance of MA devices, it is convenient to work in terms of the dimensionless quantities as expressed in equation 2 a-f:ui=Ui/Uc  Equation 2aug=Ug/Uc  2bE*=E/(Vc/L)  2cV*=V/Vc  2dK=ZVc/(UcL)  2ex*=x/L  2fwhere Uc is a characteristic sheath gas velocity, and L and Vc are the characteristic length and voltage difference, respectively. A convenient value of Uc is the average sheath gas velocity into the analyzing region. The dimensionless ion velocity may be written as equation 3:ui(x*)=uR(x*)+KE*(x*)  Equation 3.For calculation purposes, if it further assumed that the sheath gas flow is idea, in the sense that both the ug(x*) and E*(x*) vector fields given by the gradient of a scalar potential governed by the Laplace equation. So, in order to explore various MA designs one needs an efficient way of solving the Laplace Equation. A singularity method was used in this work. In this method, N singularities (line singularities for 2D; ring and/or point singularities for axi-symmetrical) are positioned outside of; but close to the analyzing region. N equations for the N unknown singularity source strengths are provided by specifying the boundary conditions at N points on the boundary of the analyzing region. The N simultaneous linear equations are then solved for the N unknown singularity strengths. Two calculations are required, one each for E* and ug. The Laplace equation must be solved subject to a set of boundary conditions for a given device. In the case of E*, the voltage is usually specified for the various elements. The boundary conditions for flow field require that a there is a certain flow rate into the analyzing region and the walls of the analyzing region are impenetrable to the gas except at inlets and outlets where there may be a net flux of gas. Knowing these singularity strengths, the field (E*(x*) or ug(x*)) at any point inside the analyzing region can be found by superimposing the fields of the N singularities. While a singularity method was used in the work that follows there are many ways of solving the Laplace Equation known to those skilled in the art. The particular method of solution is not germane to the invention. Suffice it to say that by solving the Laplace Equation in dimensionless form using the above dimensionless quantities, the trajectories of ions with various mobilities can be traced through the analyzing region starting at the inlet in explicit terms of K instead of Z. The trajectories are calculated by repetitive use of Equation 3 as follows. The velocity at the inlet of an ion with a given K is first calculated by evaluating the E* and ug at the inlet point and applying Equation 3. The ions are then allowed to move to a new point a small distance in the direction of the inlet ion velocity. E* and ug are then calculated at this new point and a new ui is found from Equation 3. The ion then moves a short distance based on the new ui and the process is repeated until the ion strikes a wall, an outlet or passes out of the analyzing region. Knowing the inlet width and flow rate, and the outlet width and flow rate the range of K (ΔK) for ions that can be collected at the outlet can be determined for any configuration of a device.
The ion trajectories (160) are shown as solid lines emanating from the inlet (130) for the prior art DMA in terms of K in FIG. 1. An ion mobility spectrum is produced by measuring the signal (current) of ions reaching the outlet (140) as a function of the voltage difference (Vc) between the plates. In dimensionless terms, such a mobility spectrum can be cast in terms of a “Transmission” as a function of K. The transmission is caressed in terms of the percentage of ions of a certain K input into the MA which can reach the outlet and is independent of rate of input of these ions at the inlet. The signal in the ion mobility spectrum would then be proportional to the rate of input of K-ions multiplied by the transmission of that K-ion. The reason for using dimensionless quantities in this analysis is that while E(x) varies with Vc, E* is a function only of the device geometry. The dimensionless voltage (V*) has a value of 1 on the top plate (110) and 0 on the bottom plate (120). After calculating the ion trajectories in terms of K, we find that ions within a small range of a certain K, called Ko, can reach the outlet. The corresponding values of ion mobilities that can reach the outlet (Zo) are found by inverting Eqn. 2d to become equation 4:Zo=KoUcL/Vc  Equation 4.Hence, once Ko is determined, the ion mobilities that reach the outlet can be calculated for a given voltage difference between the plates (Vc).
In FIG. 1, the ions follow trajectories (160) from the inlet (130) on the top plate (110) to the bottom plate (120). The slope of the trajectory line decreases with decreasing ion mobility. Hence, high mobility ions strike the bottom plate upstream from the lower mobility ions. The outlet (140), located on the bottom plate (120), is positioned to collect ions of the desired mobility.
A mobility spectrum may contain one or more peaks, corresponding to each of the ion species present in the inlet sample. The performance of a device is expressed in terms of Resolution (Res) per equation 5:Res=Zmean/ΔZ  Equation 5.where Zmean is the mobility corresponding to the center of a given peak. For DMA's, ΔZ is the width of the peak at half the height of the peak. For CMA's ΔZ is the Z-difference between no signal and full signal. Alternatively, the resolution can be expressed in terms of K instead of Z:Res=Kmean/ΔK  Equation 6.Where Kmean is the value of K at the center of a peak. For DMA's, ΔK is the width of the transmission peak at half-height. For CMA's, ΔK is the K-difference between no transmission and full transmission. The resolution may also be expressed as the inverse of the definitions given above. This inverse resolution (IRes) is expressed as in equation 7:IRes=100/Res  Equation 7.
The larger the value of Res, the smaller is the value of IRes. So a high resolution would mean a small IRes. It is desirable to have the resolution as high as possible. In other words, it is desirable to have the width at half height of a peak (ΔZ, ΔK) to be as small as possible. If the resolution is low, it is possible that when two ions with similar mobilities are present, their ion mobility spectrum peaks may be so close that they merge into a single peak and their individual identities would not be detected. A high resolution device, on the other hand, would be able to show, or resolve, the two peaks, making identification of the individual ion species easier. The resolution of a device is affected by several factors including the widths and flows of the inlet and outlet, ion spread in the analyzing region resulting from diffusion and sheath gas irregularities such as turbulence and boundary layer effects. As was shown in Rosell-Llompart et al., Minimization of the diffusive broadening of ultrafine particles in differential mobility analyzers, in Synthesis and Characterization of Ultrafine Particles, pp. 109-114 (1993), it is desirable to have the sheath gas flow rate as high as possible in order to minimize diffusion spreading and boundary layer effects. The rate of sheath gas flow is usually characterized by the Reynolds Number (Re)Re=2L Ug,ave/ν  Equation 8Where ν is the kinematic viscosity of the gas and Ug,ave is the average gas velocity in a channel. A high sheath gas flow rate means the Reynolds number should be as high as possible to minimize diffusive effects. There are, however, limitations on the maximum sheath gas flow rate before the onset of turbulence. Achieving high Reynolds number flow without turbulence is difficult. de Juan and de la Mora (J. Aerosol Sci. 29, 617-626, 1998) showed how to achieve Reynolds numbers as high as 5000 in a device similar to that disclosed by Winklmair, et.al., A New Electro-mobility Spectrometer for the Measurement of Aerosol Size Distributions in the Size Range from 1 to 1,000 Nanometers, J. Aerosol Sci., Vol. 22, pp 289-296 (1991). Some aspects of achieving high Reynolds numbers while avoiding turbulence were disclosed by de la Mora, et.al in U.S. Pat. Nos. 5,869,831 and 5,936,242 by reducing perturbations in the inlet sheath gas flow by using stages of laminarizing screens and filters followed by rapid acceleration of the sheath gas prior to introduction into the analyzing region. Using this technique Reynolds numbers of the order of 35,000 were attained before the onset of turbulence.
The MA shown in FIG. 1 may be described as two dimensional (2D) because the analyzing region is between two parallel plates. An alternative to this 2D design is one in which the top and bottom plates are replaced by concentric cylinders. This alternative design is called “axi-symmetric” (AS) because it is symmetrical about the cylinder center line (axi). The trajectories of the ions in the AS design are schematically the same as in the 2D design. It should be noted that in the prior art MA devices all ions within the analyzing region move continuously from the top plate to the bottom plate. This means that the velocities of the ions, as they move along their trajectories, are at all points in the analyzing region greater than zero.
A few previous authors have investigated non-traditional MA configurations with the goal of achieving certain desirable operational advantages. Loscertales, Drift Differential Mobility Analyzer, J Aerosol Sci., Vol. 29, pp1117-1139, 1998 described a DMA device in which an electric field antiparallel to the fluid flow is imposed in addition to the traditional transverse field. The main novelty of the Loscertales device stems from the fact that it substitutes the traditional two-element DMA geometry by one with effectively an infinite number of infinitesimal elements. In the particular case where the electric and fluid flow fields are both spatially uniform Loscertales demonstrates the possibility of singularly high resolving powers. His design uses two surfaces supporting constant tangential electric fields rather than constant voltages. A working device based on the Loscertales principles, however, has yet to be built. Tammet, The Limits of Air Ion Mobility Resolution, Proc. 11th Int. Conf. Atmos. Electr., NASA, MSFC, Alabama, 626-629, 1999, described a working device called an Inclined Grid Mobility Analyzer (IGMA) in an attempt to simulate the fields in a Loscertales DMA. In the IGMA, the sheath gas passes through two inclined electrified screens that are held at different voltages. The voltage on the screens generates the electrical field for the analyzing region located between the screens. The interference of the sheath gas flow as it passes through the screens, however, produces a complicated aerodynamic flow (turbulence) which is one of the shortcomings of the device. The screens in the Tammet device are what may be called perturbing screens. A perturbing screen is one in which introduces turbulence in the analyzing region. A non-perturbing screen is one which is downstream of the analyzing region or is in a position upstream of the analyzing region where the sheath gas flow channel has a wider area and substantially smaller Reynolds Number, so turbulence is not generated or if turbulence is generated it decays substantially downstream of the screen and has little if any affect in the analyzing region. The Tammet device has a large voltage jump at the inlet resulting in significant losses of ions before they can enter the analyzing region. To moderate these losses, Tammet uses an inlet opening that is much wider than is typical for the traditional MA devices such as that shown in FIG. 1. Indeed, if the inlet in the Tammet device were narrow, that is similar in width to those in traditional MA devices, few if any ions would be able to enter the analyzing region. With a few other relevant exceptions (Flagan, R. C. and Zhang, S. H., 1997, Radial differential mobility analyzer, U.S. Pat. No. 5,596,136; J. Fernandez de la Mora, Diffusion broadening in converging differential mobility analyzers, J. Aerosol Science, 33, 411-437, 2002), traditional DMA analyzing region designs have tended to be limited first geometrically, to parallel or coaxial cylindrical geometries. Second, except for Loscertale's Drift DMA, which is still only conceptual, almost all DMA designs involve two elements only. Third, the ion inlet and outlet have always been located in different elements. From these later two restrictions alone two serious complicating features follow inevitably. If a voltage difference between the elements is necessary to establish a field in the analyzing region, while the inlet is in one electrode and the outlet is located on the other, the inlet and outlet lines need to be at different voltages. This then precludes caving the analyzing region of the DMA from a single piece of metal, which would be ideal for achieving a precise alignment. A second related problem is that the sampled aerosol is often at or near ground (such as in atmospheric sampling, or when sampling from aerosol generators that cannot be floated), while the aerosol detector often also needs to be at or near ground. Consequently, a high voltage jump needs to be imposed either on the inlet of the outlet, and the associated fields lead to considerable sample losses, especially in the nanometer size range. This problem is particularly acute in cases involving the use of two or more MAs in tandem, since the losses associated to each voltage jump grow exponentially with the number of MA stages. In light of this, it would be desirable to have MA devices in which the voltage difference between the inlet and outlet is as small as possible.